Background

This document has nls (non-linear least squares) regression fits to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(\tau\): biomass productivity trend, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(B\) with increasing \(STDAGE_{t2}\), thus, weighted-nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}^2\) in equal-sample sized stand age bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.

Model selection is used to determine the best fitting models, which is implemented in three parts. The first part selects the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).

model 1: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

model 2: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)

sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)

Lastly, model selection part 3, fits three similar models to model selection part one, but uses the Log-Normal functional form. The Log-Normal equation fits more of “hump-shaped” curve which allows for a decrease in biomass at old stand ages. Two Log-normal models are fitted: 1) the simple model, and 2) the \(\alpha\) model: account for growth compensation due to plot biomass loss.

model 4: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 5: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

Note:

This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval

This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6880     1758.3                                
## 2   6827     1549.6 53 208.71  17.349 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 74579.98
## 2     2 73289.04
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.67452    0.17477    3.86 0.000115 ***
## alpha   0.84798    0.02771   30.60  < 2e-16 ***
## A     393.99644   24.36456   16.17  < 2e-16 ***
## k     172.58285   11.68008   14.78  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4764 on 6827 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.999e-06
##   (53 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   6827     1549.6                             
## 2   6826     1548.9  1 0.76688  3.3797 0.06605 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 73289.04
## 2    2a 73287.66
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   6.980e-01  1.765e-01   3.954 7.78e-05 ***
## alpha 8.460e-01  2.759e-02  30.667  < 2e-16 ***
## A     4.393e+02  4.894e+01   8.977  < 2e-16 ***
## k     2.106e+02  3.476e+01   6.058 1.46e-09 ***
## p     9.141e-03  4.824e-03   1.895   0.0581 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4763 on 6826 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 8.999e-06
##   (53 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6878     1726.3                                
## 2   6825     1505.9 53 220.44  18.851 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 73287.66
## 2     3 74457.48
## 3     4 73097.37
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.88132    0.18708   4.711 2.52e-06 ***
## alpha   0.84265    0.02664  31.627  < 2e-16 ***
## a      37.96496    1.70575  22.257  < 2e-16 ***
## b     102.86051    4.64467  22.146  < 2e-16 ***
## c     114.69627    4.21714  27.198  < 2e-16 ***
## d       0.92535    0.03937  23.504  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4697 on 6825 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (53 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1  22648     8866.6                                  
## 2  18856     6793.7 3792 2072.9  1.5173 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 236627.9
## 2     2 196558.7
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.36931    0.11282   3.273  0.00106 ** 
## alpha   0.70673    0.02261  31.251  < 2e-16 ***
## A     170.68000    4.81077  35.479  < 2e-16 ***
## k      63.81081    1.90831  33.438  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6002 on 18856 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 6.72e-06
##   (3825 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  18856     6793.7                                
## 2  18855     6696.2  1  97.51  274.57 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 196558.7
## 2    2a 196288.1
## 3    2b 196519.3
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   3.120e-01  1.094e-01   2.853  0.00434 ** 
## alpha 7.206e-01  1.903e-02  37.868  < 2e-16 ***
## A     2.250e+02  1.037e+01  21.689  < 2e-16 ***
## k     1.207e+02  8.513e+00  14.184  < 2e-16 ***
## p     4.607e-02  2.146e-03  21.469  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5959 on 18855 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 7.664e-06
##   (3825 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1  22646     8719.0                                  
## 2  18854     6480.3 3792 2238.6  1.7176 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 196288.1
## 2     3 236251.5
## 3     4 195672.2
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.50006    0.11585   4.317 1.59e-05 ***
## alpha   0.78377    0.01478  53.030  < 2e-16 ***
## a      23.58921    0.68133  34.622  < 2e-16 ***
## b      78.95623    2.10236  37.556  < 2e-16 ***
## c     109.35069    2.95706  36.979  < 2e-16 ***
## d       1.19460    0.02909  41.065  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5863 on 18854 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3825 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7303     1344.5                                
## 2   7237     1180.5 66 163.99  15.232 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 79950.98
## 2     2 78502.49
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.12684    0.11521   1.101    0.271    
## alpha   0.82089    0.02646  31.029   <2e-16 ***
## A     489.30464   25.34219  19.308   <2e-16 ***
## k     148.21326    8.79104  16.860   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4039 on 7237 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.733e-06
##   (66 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   7237     1180.5                           
## 2   7236     1180.4  1 0.066948  0.4104 0.5218
##   model      AIC
## 1     2 78502.49
## 2    2a 78504.07
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.12684    0.11521   1.101    0.271    
## alpha   0.82089    0.02646  31.029   <2e-16 ***
## A     489.30464   25.34219  19.308   <2e-16 ***
## k     148.21326    8.79104  16.860   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4039 on 7237 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.733e-06
##   (66 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7301     1330.8                                
## 2   7235     1163.2 66 167.61  15.796 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 78502.49
## 2     3 79879.95
## 3     4 78399.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.18210    0.11745    1.55    0.121    
## alpha   0.82346    0.02507   32.84   <2e-16 ***
## a      30.30540    2.04883   14.79   <2e-16 ***
## b     165.27194    7.48047   22.09   <2e-16 ***
## c     136.54936    9.18585   14.87   <2e-16 ***
## d       1.34424    0.06314   21.29   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.401 on 7235 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (66 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   5841     1995.4                                  
## 2   4838     1497.5 1003 497.98  1.6041 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 62741.48
## 2     2 51878.97
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.14016    0.19526   0.718    0.473    
## alpha   0.83989    0.04203  19.982   <2e-16 ***
## A     419.45906   34.98507  11.990   <2e-16 ***
## k     179.10235   16.49883  10.855   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5563 on 4838 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.159e-06
##   (1004 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   4838     1497.5                           
## 2   4837     1497.4  1 0.059639  0.1927 0.6607
##   model      AIC
## 1     2 51878.97
## 2    2a 51880.78
## 3    2b 51860.89
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.20453    0.20079   1.019    0.308    
## alpha   0.86125    0.04247  20.280  < 2e-16 ***
## A     245.89228   25.01931   9.828  < 2e-16 ***
## k      74.26959   10.35307   7.174 8.41e-13 ***
## s       1.25896    0.06043  20.833  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5552 on 4837 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.132e-06
##   (1004 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   5839     1955.8                                  
## 2   4836     1444.1 1003 511.72  1.7085 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 51860.89
## 2     3 62628.31
## 3     4 51707.33
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.21911    0.19834   1.105    0.269    
## alpha   0.86098    0.03492  24.656   <2e-16 ***
## a      25.85799    1.56357  16.538   <2e-16 ***
## b     113.29766    5.56958  20.342   <2e-16 ***
## c     102.72706    4.47856  22.938   <2e-16 ***
## d       1.02269    0.04585  22.304   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5465 on 4836 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1004 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   9996     1894.8                                  
## 2   8721     1571.7 1275 323.07   1.406 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1     1 104296.40
## 2     2  90861.83
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.09397    0.10097   0.931    0.352    
## alpha   0.75907    0.02717  27.941   <2e-16 ***
## A     246.44415    8.71838  28.267   <2e-16 ***
## k      71.27405    3.32328  21.447   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4245 on 8721 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.84e-06
##   (1281 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   8721     1571.7                          
## 2   8720     1571.5  1 0.17079  0.9477 0.3303
##   model      AIC
## 1     2 90861.83
## 2    2a 90862.88
## 3    2b 90829.10
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.11062    0.10156   1.089    0.276    
## alpha   0.76461    0.02731  27.993   <2e-16 ***
## A     180.02124    8.11605  22.181   <2e-16 ***
## k      39.98216    2.53118  15.796   <2e-16 ***
## s       1.35814    0.06011  22.594   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4237 on 8720 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.045e-06
##   (1281 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   9994     1868.9                                  
## 2   8719     1536.5 1275 332.39  1.4794 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1    2b  90829.10
## 2     3 104162.96
## 3     4  90668.25
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "223", , value =
## structure(list(: provided 32 variables to replace 31 variables
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.11966    0.10084   1.187    0.235    
## alpha   0.76968    0.02605  29.541   <2e-16 ***
## a      31.40344    1.93795  16.204   <2e-16 ***
## b     103.16970    3.44725  29.928   <2e-16 ***
## c     102.24785    4.00685  25.518   <2e-16 ***
## d       1.21271    0.05204  23.301   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4198 on 8719 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1281 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  12796     4809.1                                 
## 2  12522     4175.6 274 633.55  6.9341 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 141420.6
## 2     2 137621.6
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.25689    0.14587   8.617   <2e-16 ***
## alpha   0.58948    0.01827  32.263   <2e-16 ***
## A     219.72489    7.22935  30.393   <2e-16 ***
## k      48.95756    1.56970  31.189   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5775 on 12522 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.264e-06
##   (318 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_231,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12522     4175.6                                
## 2  12521     3965.0  1 210.56  664.91 < 2.2e-16 ***
## 3  12520     3860.0  1 104.98  340.50 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 137621.6
## 2    2a 136975.5
## 3    2b       NA
## 4    2c 136641.4
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   2.160e+00  1.852e-01   11.66   <2e-16 ***
## alpha 8.060e-01  1.026e-02   78.53   <2e-16 ***
## A     1.278e+02  4.542e+00   28.14   <2e-16 ***
## k     3.209e+01  8.753e-01   36.66   <2e-16 ***
## p     2.013e-01  7.285e-03   27.63   <2e-16 ***
## s     2.406e+00  1.056e-01   22.79   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5553 on 12520 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 9.748e-06
##   (318 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  12794     4770.2                                 
## 2  12520     3858.0 274  912.2  10.804 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 136641.4
## 2     3 141320.7
## 3     4 136634.9
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     2.12172    0.18310   11.59   <2e-16 ***
## alpha   0.80660    0.01021   79.02   <2e-16 ***
## a      26.09875    0.76750   34.01   <2e-16 ***
## b      97.84378    3.83032   25.55   <2e-16 ***
## c     101.68624    5.56650   18.27   <2e-16 ***
## d       1.38333    0.04701   29.43   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5551 on 12520 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (318 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  13052     7462.8                                 
## 2  12738     6773.3 314 689.45  4.1293 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 146999.4
## 2     2 143248.7
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.95734    0.16586   5.772 8.02e-09 ***
## alpha   0.63553    0.01913  33.225  < 2e-16 ***
## A     211.21385    8.51246  24.812  < 2e-16 ***
## k      45.87774    1.81485  25.279  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7292 on 12738 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.86e-06
##   (425 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_232,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12738     6773.3                                
## 2  12737     6293.4  1  479.9  971.25 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 143248.7
## 2    2a 142314.3
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   1.542e+00  1.891e-01   8.155 3.83e-16 ***
## alpha 8.373e-01  9.828e-03  85.188  < 2e-16 ***
## A     6.501e+02  1.211e+02   5.369 8.07e-08 ***
## k     3.806e+02  8.633e+01   4.408 1.05e-05 ***
## p     3.491e-02  5.787e-03   6.033 1.65e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7029 on 12737 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.192e-06
##   (425 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  13050     7396.2                                 
## 2  12736     6127.9 314 1268.3  8.3946 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 142314.3
## 2     3 146886.4
## 3     4 141976.7
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   1.603e+00  1.888e-01   8.493   <2e-16 ***
## alpha 8.711e-01  8.328e-03 104.597   <2e-16 ***
## a     3.092e+01  1.000e+00  30.914   <2e-16 ***
## b     1.000e+02  4.613e+00  21.687   <2e-16 ***
## c     1.067e+02  7.018e+00  15.209   <2e-16 ***
## d     1.328e+00  5.460e-02  24.323   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6936 on 12736 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (425 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1339     479.03                                
## 2   1278     328.82 61 150.21  9.5706 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15098.92
## 2     2 14148.58
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.43586    0.41265   1.056    0.291    
## alpha   0.66378    0.05394  12.306  < 2e-16 ***
## A     515.74272   88.00272   5.861 5.86e-09 ***
## k     168.06395   32.33547   5.198 2.35e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5072 on 1278 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.019e-06
##   (62 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1278     328.82                           
## 2   1277     328.80  1 0.019445  0.0755 0.7835
##   model      AIC
## 1     2 14148.58
## 2    2a 14150.50
## 3    2b 14150.16
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.43586    0.41265   1.056    0.291    
## alpha   0.66378    0.05394  12.306  < 2e-16 ***
## A     515.74272   88.00272   5.861 5.86e-09 ***
## k     168.06395   32.33547   5.198 2.35e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5072 on 1278 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.019e-06
##   (62 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1337     478.27                                
## 2   1276     328.64 61 149.63   9.524 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 14148.58
## 2     3 15100.79
## 3     4 14151.88
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.43586    0.41265   1.056    0.291    
## alpha   0.66378    0.05394  12.306  < 2e-16 ***
## A     515.74272   88.00272   5.861 5.86e-09 ***
## k     168.06395   32.33547   5.198 2.35e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5072 on 1278 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.019e-06
##   (62 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95765, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.034, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   2284     617.34                                 
## 2   1780     393.55 504 223.79  2.0084 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24037.04
## 2     2 18553.35
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.28799    0.28715   1.003    0.316    
## alpha   0.72025    0.06709  10.736   <2e-16 ***
## A     258.89604   25.66614  10.087   <2e-16 ***
## k     100.18384   11.66369   8.589   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4702 on 1780 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.7e-06
##   (506 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1780     393.55                          
## 2   1779     393.43  1 0.11381  0.5146 0.4732
##   model      AIC
## 1     2 18553.35
## 2    2a 18554.83
## 3    2b 18534.36
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.33240    0.29056   1.144    0.253    
## alpha   0.73290    0.06789  10.796   <2e-16 ***
## A     147.26267   13.36288  11.020   <2e-16 ***
## k      38.77548    3.46207  11.200   <2e-16 ***
## s       1.70982    0.15327  11.155   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4676 on 1779 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 3.685e-06
##   (506 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1   2282     595.32                                 
## 2   1778     380.67 504 214.65  1.9892 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 18534.36
## 2     3 23957.97
## 3     4 18498.01
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.31661    0.28498   1.111    0.267    
## alpha  0.72100    0.06578  10.961  < 2e-16 ***
## a     26.74983    3.84702   6.953 4.99e-12 ***
## b     93.30998    7.40246  12.605  < 2e-16 ***
## c     99.58965    6.91160  14.409  < 2e-16 ***
## d      1.09752    0.09364  11.720  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4627 on 1778 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (506 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96707, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.905, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    708     336.70                                
## 2    664     256.81 44 79.888  4.6944 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7311.058
## 2     2 6846.514
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.1773     0.4342  -0.408    0.683    
## alpha   0.5661     0.0918   6.167 1.21e-09 ***
## A     194.5053    29.8795   6.510 1.49e-10 ***
## k      60.1946    10.3564   5.812 9.57e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6219 on 664 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.577e-06
##   (46 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    664     256.81                              
## 2    663     253.78  1 3.0389  7.9392 0.004982 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 6846.514
## 2    2a 6840.562
## 3    2b 6847.996
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau    -0.083028   0.451857  -0.184  0.85427    
## alpha   0.578714   0.085314   6.783 2.60e-11 ***
## A     267.977416  86.436118   3.100  0.00202 ** 
## k     119.684829  58.411617   2.049  0.04086 *  
## p       0.032739   0.008268   3.959 8.32e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6187 on 663 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.866e-06
##   (46 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    706     321.06                                
## 2    662     239.34 44 81.727  5.1376 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 6840.562
## 2     3 7281.242
## 3     4 6803.432
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.18595    0.41602  -0.447    0.655    
## alpha  0.64304    0.07575   8.489  < 2e-16 ***
## a     22.55850    2.84602   7.926  9.6e-15 ***
## b     75.97867    8.53695   8.900  < 2e-16 ***
## c     59.50943    5.44816  10.923  < 2e-16 ***
## d      0.99855    0.11429   8.737  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6013 on 662 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (46 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93732, p-value = 3.81e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.7344, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    155     28.883                            
## 2    151     26.739  4 2.1446  3.0278 0.01951 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1995.769
## 2     2 1953.364
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)   
## tau     -0.08413    1.26662  -0.066  0.94713   
## alpha    0.75308    0.24838   3.032  0.00286 **
## A     6807.62250 2948.62354   2.309  0.02231 * 
## k     1327.87742  443.91819   2.991  0.00325 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4208 on 151 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 4.033e-06
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    151     26.739                             
## 2    150     25.778  1 0.96109  5.5926 0.01932 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 1953.364
## 2    2a 1949.690
## 3    2b       NA
## 4    2c       NA
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "263", , value =
## structure(list(: provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "263", , value =
## structure(list(: provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "263", , value =
## structure(list(: provided 32 variables to replace 31 variables
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau   -1.116e-02  1.317e+00  -0.008  0.99325    
## alpha  8.636e-01  2.398e-01   3.601  0.00043 ***
## A      2.123e+04  2.453e+04   0.866  0.38806    
## k      5.512e+03  6.778e+03   0.813  0.41741    
## p      2.773e-03  2.618e-03   1.059  0.29123    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4145 on 150 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.861e-06
##   (4 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    153     30.979                            
## 2    149     28.736  4 2.2433   2.908 0.02364 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 1949.690
## 2     3 2010.835
## 3     4 1968.528
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau   -1.116e-02  1.317e+00  -0.008  0.99325    
## alpha  8.636e-01  2.398e-01   3.601  0.00043 ***
## A      2.123e+04  2.453e+04   0.866  0.38806    
## k      5.512e+03  6.778e+03   0.813  0.41741    
## p      2.773e-03  2.618e-03   1.059  0.29123    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4145 on 150 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.861e-06
##   (4 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94849, p-value = 1.811e-05
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.165, p-value = 0.03038
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    214     67.657                          
## 2    211     67.104  3 0.55338    0.58 0.6287
##   model      AIC
## 1     1 2322.942
## 2     2 2308.904
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## tau    -0.81309    0.95259  -0.854   0.3943  
## alpha  -0.08192    0.30561  -0.268   0.7889  
## A     261.64141  103.82091   2.520   0.0125 *
## k     144.81331   58.56682   2.473   0.0142 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5639 on 211 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.783e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    211     67.104                            
## 2    210     67.101  1 0.0029778  0.0093 0.9232
##   model      AIC
## 1     2 2308.904
## 2    2a 2310.894
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## tau    -0.81309    0.95259  -0.854   0.3943  
## alpha  -0.08192    0.30561  -0.268   0.7889  
## A     261.64141  103.82091   2.520   0.0125 *
## k     144.81331   58.56682   2.473   0.0142 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5639 on 211 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.783e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Error in nls(f_4, data = G_313, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: false convergence (8)
##   model      AIC
## 1     2 2308.904
## 2     3 2310.402
## 3     4       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## tau    -0.81309    0.95259  -0.854   0.3943  
## alpha  -0.08192    0.30561  -0.268   0.7889  
## A     261.64141  103.82091   2.520   0.0125 *
## k     144.81331   58.56682   2.473   0.0142 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5639 on 211 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.783e-06
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91253, p-value = 6.107e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.3057, p-value = 0.1916
## alternative hypothesis: two.sided

predict and plot

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in nls(f_1, data = G_322, start = c(tau = tau.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) : 
##   object 'nls_322.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    327     230.98                         
## 2    309     216.02 18 14.961  1.1889 0.2683
##   model      AIC
## 1     1 3395.864
## 2     2 3234.791
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.5667     0.9405  -0.603 0.547218    
## alpha   0.7128     0.1779   4.008  7.7e-05 ***
## A      78.9918    21.5520   3.665 0.000291 ***
## k      16.5318     5.5582   2.974 0.003168 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8361 on 309 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.565e-06
##   (18 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_331,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    309     216.02                                
## 2    308     204.91  1 11.109  16.698 5.597e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 3234.791
## 2    2a 3220.267
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5777     0.4868  -3.241  0.00132 ** 
## alpha   0.8611     0.1216   7.079 9.87e-12 ***
## A     314.6391   431.8195   0.729  0.46678    
## k     373.9015   734.0968   0.509  0.61088    
## p       0.1303     0.1590   0.820  0.41313    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8157 on 308 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 4.316e-06
##   (18 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Error in nls(f_4, data = G_331, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1    2a 3220.267
## 2     3 3396.105
## 3     4       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5777     0.4868  -3.241  0.00132 ** 
## alpha   0.8611     0.1216   7.079 9.87e-12 ***
## A     314.6391   431.8195   0.729  0.46678    
## k     373.9015   734.0968   0.509  0.61088    
## p       0.1303     0.1590   0.820  0.41313    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8157 on 308 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 4.316e-06
##   (18 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88574, p-value = 1.515e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.0304, p-value = 2.059e-12
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Error in nls(f_1, data = G_332, start = c(tau = tau.start, A = A.start,  : 
##   singular gradient
##   model      AIC
## 1     1       NA
## 2     2 2126.913
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     0.7647     1.9348   0.395  0.69310   
## alpha   0.8049     0.2993   2.689  0.00779 **
## A     386.0240   375.6275   1.028  0.30539   
## k     267.8564   281.9470   0.950  0.34329   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8048 on 192 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.494e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: does not fit
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 2126.913
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     0.7647     1.9348   0.395  0.69310   
## alpha   0.8049     0.2993   2.689  0.00779 **
## A     386.0240   375.6275   1.028  0.30539   
## k     267.8564   281.9470   0.950  0.34329   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8048 on 192 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.494e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    225     139.58                         
## 2    190     115.51 35 24.075  1.1315 0.2946
##   model      AIC
## 1     2 2126.913
## 2     3 2445.978
## 3     4 2116.424
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.1813     2.1740   0.543 0.587502    
## alpha   0.8182     0.2392   3.421 0.000763 ***
## a      25.7860    12.4200   2.076 0.039224 *  
## b      77.3563    65.5343   1.180 0.239319    
## c     143.4271   153.2697   0.936 0.350573    
## d       1.0825     0.7444   1.454 0.147538    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7797 on 190 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (36 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88031, p-value = 2.28e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.9431, p-value = 7.689e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6772     1333.1                                
## 2   6748     1126.2 24 206.94  51.665 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 71776.53
## 2     2 70468.36
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.80294    0.16480   4.872 1.13e-06 ***
## alpha   0.81438    0.02205  36.934  < 2e-16 ***
## A     397.95049   22.43035  17.742  < 2e-16 ***
## k     178.49005   10.18977  17.517  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4085 on 6748 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.987e-06
##   (26 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   6748     1126.2                              
## 2   6747     1121.6  1 4.5558  27.405 1.7e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 70468.36
## 2    2a 70442.99
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     0.718055   0.159681   4.497 7.01e-06 ***
## alpha   0.819495   0.022230  36.864  < 2e-16 ***
## A     318.006672  19.444264  16.355  < 2e-16 ***
## k     112.299842  11.187675  10.038  < 2e-16 ***
## p      -0.034143   0.009135  -3.738 0.000187 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4077 on 6747 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.084e-06
##   (26 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6770     1322.9                                
## 2   6746     1116.9 24 205.98  51.836 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 70442.99
## 2     3 71728.53
## 3     4 70416.75
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.7253     0.1599   4.536 5.84e-06 ***
## alpha   0.8231     0.0219  37.579  < 2e-16 ***
## a      16.5607     2.7458   6.031 1.71e-09 ***
## b     150.2164    10.1830  14.752  < 2e-16 ***
## c     197.3137    23.5423   8.381  < 2e-16 ***
## d       1.6389     0.1071  15.297  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4069 on 6746 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (26 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8180     1388.9                                
## 2   8124     1275.5 56 113.39  12.897 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 90550.28
## 2     2 89408.34
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.76544    0.11795    6.49 9.11e-11 ***
## alpha   0.84668    0.03342   25.34  < 2e-16 ***
## A     256.52967    7.92961   32.35  < 2e-16 ***
## k      58.22137    2.29234   25.40  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3962 on 8124 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.65e-06
##   (58 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   8124     1275.5                              
## 2   8123     1275.5  1  0.000   0.0001 0.9932    
## 3   8123     1268.7  0  0.000                    
## 4   8122     1236.9  1 31.815 208.9052 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 89408.34
## 2    2a 89410.33
## 3    2b 89367.31
## 4    2c 89162.89
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.93249    0.12409   7.515 6.31e-14 ***
## alpha   0.84839    0.03004  28.242  < 2e-16 ***
## A     158.69784    4.45097  35.655  < 2e-16 ***
## k      38.50195    0.80166  48.028  < 2e-16 ***
## p       0.25252    0.01316  19.195  < 2e-16 ***
## s       2.97626    0.17662  16.851  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3902 on 8122 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.741e-06
##   (58 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8178     1358.7                                
## 2   8122     1234.5 56 124.24  14.597 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 89162.89
## 2     3 90374.77
## 3     4 89146.89
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.92767    0.12358   7.506 6.72e-14 ***
## alpha   0.84684    0.03017  28.068  < 2e-16 ***
## a      39.06110    1.95242  20.006  < 2e-16 ***
## b     113.70774    3.44940  32.965  < 2e-16 ***
## c      99.69266    2.70190  36.897  < 2e-16 ***
## d       1.16504    0.04168  27.949  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3899 on 8122 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (58 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    887     122.26                                
## 2    882     106.05  5 16.209  26.961 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9055.244
## 2     2 8902.357
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.01081    0.25502  -0.042    0.966    
## alpha   0.89748    0.07232  12.410  < 2e-16 ***
## A     284.32641   32.44983   8.762  < 2e-16 ***
## k      91.18874   14.26526   6.392 2.64e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3468 on 882 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.12e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    882     106.05                          
## 2    881     105.89  1 0.16567  1.3785 0.2407
##   model      AIC
## 1     2 8902.357
## 2    2a 8902.972
## 3    2b 8904.142
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.01081    0.25502  -0.042    0.966    
## alpha   0.89748    0.07232  12.410  < 2e-16 ***
## A     284.32641   32.44983   8.762  < 2e-16 ***
## k      91.18874   14.26526   6.392 2.64e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3468 on 882 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.12e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    885     121.92                                
## 2    880     105.92  5 16.008    26.6 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 8902.357
## 2     3 9056.791
## 3     4 8905.228
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.01081    0.25502  -0.042    0.966    
## alpha   0.89748    0.07232  12.410  < 2e-16 ***
## A     284.32641   32.44983   8.762  < 2e-16 ***
## k      91.18874   14.26526   6.392 2.64e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3468 on 882 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.12e-06
##   (7 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96279, p-value = 3.085e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -15.005, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1005     242.87                                
## 2    991     213.68 14 29.185  9.6678 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 10414.94
## 2     2 10205.89
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.69296    0.47940   1.445    0.149    
## alpha   0.72680    0.06767  10.740  < 2e-16 ***
## A     222.81000   29.06880   7.665 4.26e-14 ***
## k      87.09494   11.66224   7.468 1.78e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4644 on 991 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.437e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)   
## 1    991     213.68                              
## 2    990     212.16  1 1.52717  7.1264 0.00772 **
## 3    990     212.15  0 0.00000                   
## 4    989     212.13  1 0.01961  0.0914 0.76245   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 10205.89
## 2    2a 10200.76
## 3    2b 10200.72
## 4    2c 10202.63
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   5.958e-01  4.601e-01   1.295    0.196    
## alpha 7.401e-01  6.343e-02  11.668  < 2e-16 ***
## A     6.172e+03  8.849e+04   0.070    0.944    
## k     2.337e+04  5.044e+05   0.046    0.963    
## s     7.039e-01  1.105e-01   6.369  2.9e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4629 on 990 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 7.767e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Error in nls(f_4, data = G_M231, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1    2b 10200.72
## 2     3 10415.55
## 3     4       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   5.958e-01  4.601e-01   1.295    0.196    
## alpha 7.401e-01  6.343e-02  11.668  < 2e-16 ***
## A     6.172e+03  8.849e+04   0.070    0.944    
## k     2.337e+04  5.044e+05   0.046    0.963    
## s     7.039e-01  1.105e-01   6.369  2.9e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4629 on 990 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 7.767e-06
##   (14 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96083, p-value = 1.104e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.338, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3298     2133.7                                
## 2   3224     1974.0 74 159.72  3.5251 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 43707.67
## 2     2 42724.57
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     -0.34540    0.45370  -0.761    0.447    
## alpha    1.04644    0.06748  15.508  < 2e-16 ***
## A     1189.96044  176.98435   6.724 2.09e-11 ***
## k      340.28730   31.51514  10.798  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7825 on 3224 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.189e-06
##   (75 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3224     1974.0                                
## 2   3223     1944.4  1 29.586  49.041 3.038e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 42724.57
## 2    2a 42677.82
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.28026    0.46308  -0.605    0.545    
## alpha   1.09425    0.06592  16.600  < 2e-16 ***
## A     885.21824  129.06241   6.859 8.29e-12 ***
## k     183.55735   21.87074   8.393  < 2e-16 ***
## p      -0.05050    0.01100  -4.592 4.55e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7767 on 3223 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.082e-06
##   (75 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3296     2088.0                                
## 2   3222     1937.6 74 150.37  3.3791 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 42677.82
## 2     3 43640.14
## 3     4 42668.50
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.27246    0.46316  -0.588    0.556    
## alpha   1.08484    0.06781  15.997  < 2e-16 ***
## a       8.65719   10.66752   0.812    0.417    
## b     568.18274   83.89943   6.772 1.50e-11 ***
## c     556.00691  107.65155   5.165 2.55e-07 ***
## d       2.03644    0.16919  12.037  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7755 on 3222 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (75 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94605, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -16.804, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)
## 1   1983     1184.8                          
## 2   1699     1053.3 284  131.5  0.7468  0.999
##   model      AIC
## 1     1 24895.19
## 2     2 21467.37
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.6101     0.2488  -6.472 1.26e-10 ***
## alpha   0.7419     0.1061   6.995 3.79e-12 ***
## A     760.7191    97.5974   7.794 1.12e-14 ***
## k     123.2836    16.8865   7.301 4.38e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7874 on 1699 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.299e-06
##   (290 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1699     1053.3                          
## 2   1698     1053.2  1 0.07033  0.1134 0.7364
## 3   1698     1053.3  0 0.00000               
## 4   1697     1052.9  1 0.44739  0.7211 0.3959
##   model      AIC
## 1     2 21467.37
## 2    2a 21469.26
## 3    2b 21469.36
## 4    2c 21470.64
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.6101     0.2488  -6.472 1.26e-10 ***
## alpha   0.7419     0.1061   6.995 3.79e-12 ***
## A     760.7191    97.5974   7.794 1.12e-14 ***
## k     123.2836    16.8865   7.301 4.38e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7874 on 1699 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.299e-06
##   (290 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Error in nls(f_4, data = G_M261, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: singular convergence (7)
##   model      AIC
## 1     2 21467.37
## 2     3 24897.19
## 3     4       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.6101     0.2488  -6.472 1.26e-10 ***
## alpha   0.7419     0.1061   6.995 3.79e-12 ***
## A     760.7191    97.5974   7.794 1.12e-14 ***
## k     123.2836    16.8865   7.301 4.38e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7874 on 1699 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.299e-06
##   (290 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89245, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.5593, p-value = 5.407e-11
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    363     122.71                              
## 2    361     118.29  2 4.4234    6.75 0.001324 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3833.912
## 2     2 3815.658
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.9278     0.3048  -6.326 7.46e-10 ***
## alpha   0.5586     0.1422   3.929 0.000102 ***
## A     570.5201   208.8668   2.732 0.006614 ** 
## k     230.4612   110.8456   2.079 0.038312 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5724 on 361 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 1.054e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M313,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    361     118.29                            
## 2    360     116.38  1 1.9039  5.8892 0.01572 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 3815.658
## 2    2a 3811.735
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     -1.93341    0.29980  -6.449 3.63e-10 ***
## alpha    0.60955    0.13125   4.644 4.79e-06 ***
## A     1147.05673 1203.16291   0.953    0.341    
## k      672.09791  853.57636   0.787    0.432    
## p        0.02346    0.02058   1.140    0.255    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5686 on 360 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.202e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    361     120.72                                
## 2    359     114.30  2  6.413  10.071 5.553e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 3811.735
## 2     3 3831.912
## 3     4 3807.150
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "M313", , value =
## structure(list(: provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "M313", , value =
## structure(list(: provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "M313", , value =
## structure(list(: provided 32 variables to replace 31 variables
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.7796     0.3481  -5.112 5.19e-07 ***
## alpha   0.6348     0.1244   5.102 5.47e-07 ***
## a      46.4756    11.6701   3.982 8.26e-05 ***
## b     171.5834    39.2477   4.372 1.62e-05 ***
## c     174.5153    37.7519   4.623 5.29e-06 ***
## d       0.9408     0.1969   4.778 2.59e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5643 on 359 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94452, p-value = 1.864e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.87032, p-value = 0.3841
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1736     651.22                                
## 2   1714     586.85 22 64.369  8.5455 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18138.23
## 2     2 17803.52
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.79053    0.36102  -2.190   0.0287 *  
## alpha   0.61269    0.04185  14.642  < 2e-16 ***
## A     251.44405   33.32753   7.545 7.32e-14 ***
## k     114.28468   11.51206   9.927  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5851 on 1714 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.744e-06
##   (39 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'tau', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model
## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 +  : 
##   variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1714     586.85                                
## 2   1713     580.51  1 6.3473   18.73 1.593e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 17803.52
## 2    2a 17786.84
## 3    2b 17796.89
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau    -0.764169   0.364512  -2.096   0.0362 *  
## alpha   0.628230   0.040008  15.702  < 2e-16 ***
## A     322.311516  55.752829   5.781 8.80e-09 ***
## k     208.802587  46.686892   4.472 8.24e-06 ***
## p       0.044015   0.007603   5.789 8.39e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5821 on 1713 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.868e-06
##   (39 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1734     645.18                                
## 2   1712     573.25 22  71.93  9.7645 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 17786.84
## 2     3 18126.02
## 3     4 17767.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.7928     0.3549  -2.234   0.0256 *  
## alpha   0.6382     0.0391  16.325  < 2e-16 ***
## a      34.1072     4.7477   7.184 1.01e-12 ***
## b     124.4318    16.2354   7.664 2.99e-14 ***
## c     222.4559    27.7327   8.021 1.92e-15 ***
## d       1.3339     0.1216  10.974  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5787 on 1712 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (39 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92621, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.3972, p-value = 6.767e-08
## alternative hypothesis: two.sided

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2617     1396.7                                
## 2   2521     1272.5 96 124.19  2.5628 3.378e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28732.83
## 2     2 27767.83
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.26046    1.02586   1.229    0.219    
## alpha   0.53094    0.05003  10.612  < 2e-16 ***
## A     151.66316   31.42990   4.825 1.48e-06 ***
## k      91.05449    7.89510  11.533  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7105 on 2521 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.095e-06
##   (96 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2521     1272.5                                
## 2   2520     1238.5  1 34.045  69.273 < 2.2e-16 ***
## 3   2520     1255.3  0  0.000                      
## 4   2519     1213.2  1 42.165  87.549 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 27767.83
## 2    2a 27701.35
## 3    2b 27735.52
## 4    2c 27651.25
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.39322    1.06063   1.314    0.189    
## alpha   0.63541    0.03940  16.126  < 2e-16 ***
## A     114.30325   24.72719   4.623 3.98e-06 ***
## k      79.86814    5.45346  14.645  < 2e-16 ***
## p       0.18745    0.01735  10.801  < 2e-16 ***
## s       2.42997    0.29534   8.228 3.02e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.694 on 2519 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.468e-06
##   (96 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2615     1381.0                                
## 2   2519     1210.8 96 170.12  3.6866 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 27651.25
## 2     3 28707.13
## 3     4 27646.37
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.40226    1.06104   1.322    0.186    
## alpha   0.63896    0.03895  16.403  < 2e-16 ***
## a      21.79948    4.55346   4.787 1.79e-06 ***
## b      83.33942   17.58868   4.738 2.28e-06 ***
## c     211.77444   20.64033  10.260  < 2e-16 ***
## d       1.25944    0.10074  12.502  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6933 on 2519 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (96 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89705, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6568, p-value = 3.212e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1753     893.12                                
## 2   1693     800.14 60 92.977  3.2788 2.611e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19820.05
## 2     2 19161.17
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     2.07826    1.90430   1.091  0.27527    
## alpha   0.65732    0.05508  11.933  < 2e-16 ***
## A     239.10787   80.05515   2.987  0.00286 ** 
## k     164.44188   18.91300   8.695  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6875 on 1693 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.84e-06
##   (61 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1693     800.14                                
## 2   1692     792.86  1  7.281  15.538 8.416e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 19161.17
## 2    2a 19147.66
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   2.271e+00  2.028e+00   1.120  0.26289    
## alpha 6.701e-01  5.109e-02  13.117  < 2e-16 ***
## A     2.886e+02  1.054e+02   2.739  0.00623 ** 
## k     2.523e+02  5.970e+01   4.226 2.50e-05 ***
## p     1.837e-02  4.045e-03   4.542 5.97e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6845 on 1692 degrees of freedom
## 
## Number of iterations to convergence: 35 
## Achieved convergence tolerance: 9.399e-06
##   (61 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1751     828.43                                
## 2   1691     714.93 60  113.5  4.4742 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 19147.66
## 2     3 19692.03
## 3     4 18974.09
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     2.57942    2.08937   1.235  0.21717    
## alpha   0.70576    0.04116  17.147  < 2e-16 ***
## a      17.84902    5.91413   3.018  0.00258 ** 
## b      86.54624   28.63656   3.022  0.00255 ** 
## c     131.86513    5.63634  23.396  < 2e-16 ***
## d       0.95766    0.04899  19.548  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6502 on 1691 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (61 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93139, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.8623, p-value = 1.16e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    443     175.53                            
## 2    346     127.58 97 47.952  1.3407 0.02999 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4440.199
## 2     2 3467.793
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.53148    0.65254  -0.814  0.41594    
## alpha   0.78101    0.09794   7.975 2.26e-14 ***
## A     127.24018   26.91846   4.727 3.32e-06 ***
## k      63.57045   21.02138   3.024  0.00268 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6072 on 346 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.418e-06
##   (101 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    346     127.58                            
## 2    345     127.58  1 0.0007233  0.0020 0.9647
## 3    345     127.57  0 0.0000000               
## 4    344     127.54  1 0.0283847  0.0766 0.7822
##   model      AIC
## 1     2 3467.793
## 2    2a 3469.791
## 3    2b 3469.768
## 4    2c 3471.690
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.53148    0.65254  -0.814  0.41594    
## alpha   0.78101    0.09794   7.975 2.26e-14 ***
## A     127.24018   26.91846   4.727 3.32e-06 ***
## k      63.57045   21.02138   3.024  0.00268 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6072 on 346 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.418e-06
##   (101 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    441     174.96                            
## 2    344     127.61 97 47.344  1.3157 0.03938 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 3467.793
## 2     3 4442.739
## 3     4 3471.887
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.53148    0.65254  -0.814  0.41594    
## alpha   0.78101    0.09794   7.975 2.26e-14 ***
## A     127.24018   26.91846   4.727 3.32e-06 ***
## k      63.57045   21.02138   3.024  0.00268 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6072 on 346 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.418e-06
##   (101 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9352, p-value = 3.254e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.1237, p-value = 9.143e-10
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    214     80.493                              
## 2    210     74.287  4  6.207  4.3866 0.001993 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2156.928
## 2     2 2123.657
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.6002     0.5167  -3.097 0.002222 ** 
## alpha   0.5061     0.1376   3.678 0.000299 ***
## A     214.3813    55.2096   3.883 0.000138 ***
## k      87.8631    23.3697   3.760 0.000221 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5948 on 210 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.127e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    210     74.287                              
## 2    209     73.670  1 0.6167  1.7497 0.187365   
## 3    209     74.208  0 0.0000                    
## 4    208     70.883  1 3.3245  9.7555 0.002043 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 2123.657
## 2    2a 2123.873
## 3    2b 2125.430
## 4    2c 2117.621
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.59170    0.50616  -3.145  0.00191 ** 
## alpha   0.55088    0.12860   4.284 2.81e-05 ***
## A     148.02788   37.19073   3.980 9.51e-05 ***
## k      66.06827    9.08317   7.274 7.00e-12 ***
## p       0.18027    0.03964   4.548 9.20e-06 ***
## s       3.03179    1.21785   2.489  0.01358 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5838 on 208 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 5.604e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    212     76.519                                
## 2    208     70.029  4 6.4896  4.8188 0.0009756 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 2117.621
## 2     3 2149.940
## 3     4 2115.028
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.6230     0.4894  -3.316 0.001077 ** 
## alpha   0.5444     0.1286   4.234 3.45e-05 ***
## a      27.4152     7.3461   3.732 0.000245 ***
## b     116.7748    26.5422   4.400 1.73e-05 ***
## c     155.6772    22.0366   7.064 2.38e-11 ***
## d       1.0356     0.1981   5.228 4.16e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5802 on 208 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (6 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92949, p-value = 1.282e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.81294, p-value = 0.4163
## alternative hypothesis: two.sided

predict and plot

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod.2 Sel.Mod.3 Best.Mod
211 Northeastern Mixed Forest 2a 4 4
212 Laurentian Mixed Forest 2a 4 4
221 Eastern Broadleaf Forest 2 4 4
222 Midwest Broadleaf Forest 2b 4 4
223 Central Interior Broadleaf Forest 2b 4 4
231 Southeastern Mixed Forest 2c 4 4
232 Outer Coastal Plain Mixed Forest 2a 4 4
234 Lower Mississippi Riverine Forest 2 2 2
242 Pacific Lowland Mixed Forest NA NA NA
251 Prairie Parkland (Temperate) 2b 4 4
255 Prairie Parkland (Subtropical) 2a 4 4
261 California Coastal Chaparral Forest and Shrub NA NA NA
262 California Dry Steppe NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest 2a 2a 2a
313 Colorado Plateau Semi-Desert 2 2 2
315 Southwest Plateau and Plains Dry Steppe and Shrub NA NA NA
321 Chihuahuan Semi-Desert NA NA NA
322 American Semidesert and Desert NA NA NA
331 Great Plains/Palouse Dry Steppe 2a 2a 2a
332 Great Plains Steppe 2 4 4
341 Intermountain Semi-Desert and Desert NA NA NA
342 Intermountain Semi-Desert NA NA NA
411 Everglades NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2a 4 4
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2c 4 4
M223 Ozark Broadleaf Forest Meadow 2 2 2
M231 Ouachita Mixed Forest 2b 2b 2b
M242 Cascade Mixed Forest 2a 4 4
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2 2 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2a 4 4
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2a 4 4
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2c 4 4
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2a 4 4
M334 Black Hills Coniferous Forest 2 2 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow 2c 4 4

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6884 2879 0.8813228 0.0350003 0.5145805 1.2480652 0.8426533 0.0007099 0.7904238 0.8948828 439.3142 343.38465 535.2437 210.56313 1.424213e+02 2.787049e+02 37.964960 34.621151 41.30877 102.86051 93.75550 111.96552 114.69627 106.42936 122.9632 0.9253478 0.8481720 1.002524
212 Laurentian Mixed Forest east 22685 9493 0.5000581 0.0134207 0.2729862 0.7271300 0.7837680 0.0002184 0.7547983 0.8127376 224.9575 204.62713 245.2879 120.74409 1.040583e+02 1.374299e+02 23.589205 22.253731 24.92468 78.95623 74.83541 83.07706 109.35069 103.55458 115.1468 1.1945977 1.1375776 1.251618
221 Eastern Broadleaf Forest east 7307 3560 0.1820966 0.0137947 -0.0481413 0.4123346 0.8234621 0.0006286 0.7743142 0.8726099 489.3046 439.62656 538.9827 148.21326 1.309803e+02 1.654463e+02 30.305398 26.289091 34.32170 165.27194 150.60803 179.93586 136.54936 118.54243 154.5563 1.3442406 1.2204710 1.468010
222 Midwest Broadleaf Forest east 5846 2589 0.2191055 0.0393389 -0.1697320 0.6079429 0.8609837 0.0012194 0.7925247 0.9294428 245.8923 196.84307 294.9415 74.26959 5.397287e+01 9.456632e+01 25.857990 22.792685 28.92330 113.29766 102.37876 124.21657 102.72706 93.94705 111.5071 1.0226878 0.9327978 1.112578
223 Central Interior Broadleaf Forest east 10006 3860 0.1196573 0.0101686 -0.0780119 0.3173264 0.7696806 0.0006788 0.7186077 0.8207536 180.0212 164.11187 195.9306 39.98216 3.502045e+01 4.494387e+01 31.403445 27.604600 35.20229 103.16970 96.41229 109.92712 102.24785 94.39348 110.1022 1.2127067 1.1106876 1.314726
231 Southeastern Mixed Forest east 12844 5935 2.1217238 0.0335259 1.7628180 2.4806297 0.8066003 0.0001042 0.7865912 0.8266093 127.7848 118.88207 136.6876 32.08778 3.037208e+01 3.380348e+01 26.098748 24.594334 27.60316 97.84378 90.33575 105.35180 101.68624 90.77504 112.5974 1.3833283 1.2911888 1.475468
232 Outer Coastal Plain Mixed Forest east 13167 6463 1.6031145 0.0356297 1.2331199 1.9731092 0.8710963 0.0000694 0.8547719 0.8874207 650.0955 412.74063 887.4504 380.55124 2.113342e+02 5.497683e+02 30.917153 28.956773 32.87753 100.04223 91.00020 109.08425 106.73662 92.98075 120.4925 1.3280105 1.2209872 1.435034
234 Lower Mississippi Riverine Forest east 1344 759 0.4358633 0.1702808 -0.3736843 1.2454108 0.6637788 0.0029096 0.5579571 0.7696004 515.7427 343.09704 688.3884 168.06395 1.046275e+02 2.315004e+02 NA NA NA NA NA NA NA NA NA NA NA NA
242 Pacific Lowland Mixed Forest pacific 85 85 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 2290 903 0.3166111 0.0812149 -0.2423245 0.8755466 0.7210025 0.0043272 0.5919852 0.8500198 147.2627 121.05407 173.4713 38.77548 3.198534e+01 4.556563e+01 26.749834 19.204673 34.29499 93.30998 78.79153 107.82843 99.58965 86.03393 113.1454 1.0975160 0.9138552 1.281177
255 Prairie Parkland (Subtropical) east 714 318 -0.1859510 0.1730759 -1.0028363 0.6309342 0.6430371 0.0057374 0.4943060 0.7917682 267.9774 98.25591 437.6989 119.68483 4.990785e+00 2.343789e+02 22.558497 16.970193 28.14680 75.97867 59.21591 92.74144 59.50943 48.81167 70.2072 0.9985515 0.7741415 1.222962
261 California Coastal Chaparral Forest and Shrub pacific 26 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 159 157 -0.0111604 1.7339910 -2.6130542 2.5907333 0.8636392 0.0575211 0.3897468 1.3375316 21233.8336 -27233.49640 69701.1637 5511.67996 -7.881182e+03 1.890454e+04 NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 -0.8130865 0.9074242 -2.6908955 1.0647226 -0.0819227 0.0933971 -0.6843616 0.5205163 261.6414 56.98230 466.3005 144.81331 2.936225e+01 2.602644e+02 NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 -1.5776899 0.2369940 -2.5356043 -0.6197756 0.8611181 0.0147981 0.6217530 1.1004832 314.6391 -535.05048 1164.3287 373.90147 -1.070578e+03 1.818381e+03 NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 1.1813235 4.7263191 -3.1069723 5.4696194 0.8182341 0.0572011 0.3464693 1.2899989 386.0240 -354.86226 1126.9103 267.85640 -2.882549e+02 8.239677e+02 25.785961 1.287256 50.28467 77.35625 -51.91195 206.62445 143.42713 -158.90159 445.7559 1.0825214 -0.3858405 2.550883
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6778 3008 0.7253080 0.0255701 0.4118408 1.0387753 0.8230698 0.0004797 0.7801339 0.8660057 318.0067 279.88978 356.1236 112.29984 9.036847e+01 1.342312e+02 16.560727 11.178056 21.94340 150.21644 130.25461 170.17827 197.31368 151.16330 243.4641 1.6388804 1.4288507 1.848910
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8186 3765 0.9276701 0.0152730 0.6854135 1.1699266 0.8468373 0.0009103 0.7876954 0.9059793 158.6978 149.97279 167.4229 38.50195 3.693050e+01 4.007340e+01 39.061096 35.233846 42.88835 113.70774 106.94603 120.46944 99.69266 94.39625 104.9891 1.1650416 1.0833293 1.246754
M223 Ozark Broadleaf Forest Meadow east 893 348 -0.0108055 0.0650335 -0.5113158 0.4897048 0.8974822 0.0052297 0.7555490 1.0394153 284.3264 220.63852 348.0143 91.18874 6.319092e+01 1.191866e+02 NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 1009 496 0.5958020 0.2116527 -0.3069975 1.4986015 0.7400715 0.0040231 0.6156024 0.8645405 6171.9126 -167471.37461 179815.1997 23371.75341 -9.664988e+05 1.013242e+06 NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest pacific 3303 3286 -0.2724568 0.2145181 -1.1805767 0.6356631 1.0848443 0.0045988 0.9518801 1.2178085 885.2182 632.16552 1138.2710 183.55735 1.406754e+02 2.264393e+02 8.657191 -12.258617 29.57300 568.18274 403.68107 732.68440 556.00691 344.93446 767.0793 2.0364416 1.7047151 2.368168
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1993 1828 -1.6100870 0.0618959 -2.0980518 -1.1221222 0.7419469 0.0112490 0.5339226 0.9499712 760.7191 569.29536 952.1428 123.28357 9.016312e+01 1.564040e+02 NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -1.7795966 0.1328687 -2.4641675 -1.0950257 0.6095510 0.0154818 0.3514346 0.8676674 1147.0567 -1219.05393 3513.1674 672.09791 -1.006524e+03 2.350720e+03 46.475597 23.525317 69.42588 171.58342 94.39917 248.76766 174.51526 100.27252 248.7580 0.9407765 0.5535532 1.328000
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1757 1757 -0.7928071 0.1259838 -1.4889727 -0.0966416 0.6382489 0.0015285 0.5615682 0.7149295 322.3115 212.96072 431.6623 208.80259 1.172333e+02 3.003719e+02 34.107158 24.795199 43.41912 124.43177 92.58849 156.27504 222.45594 168.06240 276.8495 1.3338961 1.0955011 1.572291
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2621 2611 1.4022553 1.1258016 -0.6783407 3.4828512 0.6389574 0.0015174 0.5625721 0.7153427 114.3033 65.81555 162.7910 79.86814 6.917442e+01 9.056187e+01 21.799478 12.870561 30.72840 83.33942 48.84966 117.82918 211.77444 171.30069 252.2482 1.2594430 1.0618959 1.456990
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1758 1747 2.5794211 4.3654790 -1.5186077 6.6774498 0.7057566 0.0016941 0.6250269 0.7864864 288.5627 81.92180 495.2036 252.32934 1.352299e+02 3.694287e+02 17.849018 6.249232 29.44880 86.54624 30.37942 142.71306 131.86513 120.81018 142.9201 0.9576648 0.8615742 1.053755
M334 Black Hills Coniferous Forest interior west 451 179 -0.5314777 0.4258135 -1.8149296 0.7519741 0.7810081 0.0095919 0.5883792 0.9736371 127.2402 74.29577 180.1846 63.57045 2.222468e+01 1.049162e+02 NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 -1.6230333 0.2395404 -2.5879099 -0.6581567 0.5443555 0.0165315 0.2908785 0.7978326 148.0279 74.70880 221.3470 66.06827 4.816139e+01 8.397515e+01 27.415227 12.932883 41.89757 116.77484 64.44866 169.10102 155.67721 112.23356 199.1209 1.0355782 0.6450688 1.426087

parameter variance co-variance

##                tau         alpha            a            b            c
## tau    0.035000316 -2.921063e-05 -0.221947693 -0.728760036 -0.065744162
## alpha -0.005860223  7.098746e-04  0.003592054  0.003559913 -0.001916846
## a     -0.695502026  7.903798e-02  2.909594753  2.744898036 -1.762387722
## b     -0.838674289  2.876692e-02  0.346461298 21.572996391 10.188445675
## c     -0.083330341 -1.705998e-02 -0.245000603  0.520157238 17.784272555
## d     -0.098859549 -3.553039e-03 -0.427336934  0.491775292  0.890143172
##                   d
## tau   -7.281331e-04
## alpha -3.726893e-06
## a     -2.869742e-02
## b      8.992451e-02
## c      1.477863e-01
## d      1.549931e-03
##               tau         alpha            a            b            c
## tau    0.01342069  3.715109e-05 -0.059874535 -0.214085327 -0.039346856
## alpha  0.02169785  2.184414e-04  0.001849154 -0.001227538 -0.003731858
## a     -0.75856901  1.836310e-01  0.464214943  0.744225598 -0.251206642
## b     -0.87900550 -3.950571e-02  0.519561823  4.419932394  2.866276922
## c     -0.11485816 -8.538801e-02 -0.124684042  0.461051720  8.744225998
## d     -0.07833891 -1.326805e-01 -0.327705899  0.356059946  0.861404142
##                   d
## tau   -2.640082e-04
## alpha -5.704624e-05
## a     -6.495256e-03
## b      2.177627e-02
## c      7.410033e-02
## d      8.462622e-04
##               tau         alpha            a           b           c
## tau    0.01379470  0.0001070956 -0.081089361 -0.57196291 -0.12409957
## alpha  0.03636903  0.0006285900  0.004111461 -0.00807586 -0.01450298
## a     -0.33697803  0.0800398611  4.197708988 -3.98500970 -9.12838149
## b     -0.65100249 -0.0430601920 -0.260012446 55.95748230 54.49519969
## c     -0.11502572 -0.0629729919 -0.485029853  0.79306725 84.37976186
## d     -0.06814007 -0.0540858244 -0.686476644  0.72968273  0.93876072
##                   d
## tau   -5.053030e-04
## alpha -8.561706e-05
## a     -8.880248e-02
## b      3.446326e-01
## c      5.444616e-01
## d      3.986450e-03
##               tau         alpha            a            b            c
## tau    0.03933893  0.0002002966 -0.209573026 -0.957531457 -0.066097376
## alpha  0.02891933  0.0012194057  0.004329288  0.002418565 -0.009474419
## a     -0.67578279  0.0792912841  2.444747096  3.480176571 -1.611864305
## b     -0.86680125  0.0124354458  0.399633672 31.020191294 11.440378332
## c     -0.07441064 -0.0605815744 -0.230183181  0.458648766 20.057455806
## d     -0.02685154 -0.0550250884 -0.440098893  0.354442689  0.891087602
##                   d
## tau   -2.441938e-04
## alpha -8.810269e-05
## a     -3.155161e-02
## b      9.051542e-02
## c      1.829838e-01
## d      2.102367e-03
##               tau         alpha            a            b            c
## tau    0.01016860  0.0002502204 -0.060270912 -0.236544481 -0.032910530
## alpha  0.09523783  0.0006788366  0.002643107 -0.003074269 -0.003138704
## a     -0.30841404  0.0523466584  3.755659414 -2.437359318 -3.026636229
## b     -0.68047144 -0.0342284235 -0.364841361 11.883511259  8.561117664
## c     -0.08145199 -0.0300652689 -0.389775457  0.619805518 16.054813787
## d     -0.02256004 -0.0390210645 -0.709844532  0.632382542  0.862921495
##                   d
## tau   -1.183977e-04
## alpha -5.291208e-05
## a     -7.159446e-02
## b      1.134554e-01
## c      1.799480e-01
## d      2.708608e-03
##               tau         alpha            a            b           c
## tau    0.03352594  0.0002965874 -0.098777600 -0.565450193 -0.13963326
## alpha  0.15868128  0.0001042012  0.001675951 -0.008883086 -0.01084275
## a     -0.70289589  0.2139182457  0.589052502  1.077571822 -0.90164254
## b     -0.80624756 -0.2271914222  0.366550437 14.671379950 13.77622997
## c     -0.13699859 -0.1908186409 -0.211045001  0.646119105 30.98593731
## d     -0.17654887 -0.2766022134 -0.324659485  0.612185150  0.92770625
##                   d
## tau   -0.0015195358
## alpha -0.0001327234
## a     -0.0117127976
## b      0.1102234025
## c      0.2427439102
## d      0.0022095869
##               tau         alpha            a            b            c
## tau    0.03562969  1.651537e-04 -0.148899675 -0.660064569 -0.111932405
## alpha  0.10505922  6.935795e-05  0.001501598 -0.006670866 -0.009278125
## a     -0.78874516  1.802829e-01  1.000234882  1.995880936 -1.217817267
## b     -0.75806052 -1.736431e-01  0.432620538 21.279087381 21.081493440
## c     -0.08449887 -1.587498e-01 -0.173513082  0.651217360 49.249044597
## d     -0.10994254 -2.337003e-01 -0.272208128  0.586348347  0.927165488
##                   d
## tau   -0.0011330800
## alpha -0.0001062664
## a     -0.0148641766
## b      0.1476797587
## c      0.3552588718
## d      0.0029811068
##                tau         alpha            A             k
## tau    0.170280754  0.0008129697  -18.9614855    0.06854134
## alpha  0.036523847  0.0029095786   -0.3496619   -0.18957883
## A     -0.522147814 -0.0736609156 7744.4793212 2405.81801427
## k      0.005136775 -0.1086914910    0.8454490 1045.58292504
##               tau        alpha            a           b           c
## tau    0.08121491  0.002029994 -0.394868460 -1.63497670 -0.17410264
## alpha  0.10828611  0.004327212  0.002434364 -0.01279668 -0.01152039
## a     -0.36017195  0.009619593 14.799579243 -5.51284674 -8.87541025
## b     -0.77502804 -0.026279487 -0.193586448 54.79646823 26.57701308
## c     -0.08839112 -0.025338687 -0.333798894  0.51945870 47.77027228
## d     -0.04454636 -0.008196097 -0.691606270  0.53724831  0.83196932
##                   d
## tau   -0.0011887835
## alpha -0.0000504875
## a     -0.2491473482
## b      0.3724122932
## c      0.5384666779
## d      0.0087689042
##               tau        alpha           a           b           c            d
## tau    0.17307586  0.005425805 -0.74851944 -3.22751522 -0.11247870 -0.004053604
## alpha  0.17218171  0.005737437  0.02376493 -0.07485858 -0.03241448 -0.001294910
## a     -0.63219000  0.110240301  8.09980265 10.19081895 -3.11422960 -0.137701193
## b     -0.90875608 -0.115765707  0.41943932 72.87951105 10.45617802  0.218224532
## c     -0.04962515 -0.078547042 -0.20084600  0.22481228 29.68249676  0.510187051
## d     -0.08525575 -0.149582693 -0.42335149  0.22366676  0.81936956  0.013061672
##               tau       alpha             A             k             p
## tau    1.73399103  0.02574439 -6.375772e+03  8.260465e+02 -3.628483e-04
## alpha  0.08151651  0.05752111  5.321152e+02  1.767955e+02 -3.727927e-05
## A     -0.19739056  0.09045011  6.016805e+08  1.589468e+08 -5.821608e+01
## k      0.09254944  0.10875528  9.560082e-01  4.594249e+07 -1.658691e+01
## p     -0.10524743 -0.05936953 -9.065042e-01 -9.346908e-01  6.854572e-06
##                tau        alpha             A            k
## tau    0.907424207  0.005189997   -79.0522667   -0.3329832
## alpha  0.017827693  0.093397146     1.4336847   -0.3263735
## A     -0.799326696  0.045185804 10778.7812606 3608.3755944
## k     -0.005968503 -0.018234608     0.5934378 3430.0727759
##               tau        alpha             A             k             p
## tau    0.23699401 -0.002182051 -8.560042e+01 -1.030075e+02  2.051283e-02
## alpha -0.03684627  0.014798085  3.791168e+00  6.785294e+00 -7.791469e-04
## A     -0.40719732  0.072171874  1.864681e+05  3.133164e+05 -6.735300e+01
## k     -0.28823494  0.075982322  9.883881e-01  5.388981e+05 -1.143665e+02
## p      0.26508716 -0.040294750 -9.812654e-01 -9.801155e-01  2.526599e-02
##               tau       alpha            a            b             c
## tau    4.72631913  0.05249845 -23.05980787  -68.9207833    -7.0927740
## alpha  0.10096774  0.05720114  -0.01641209   -1.1085700    -2.1816517
## a     -0.85403218 -0.00552512 154.25521616  142.8292819  -486.0487750
## b     -0.48374914 -0.07072815   0.17548049 4294.7408443  8665.4727248
## c     -0.02128621 -0.05951506  -0.25533111    0.8627155 23491.5891406
## d      0.01871121 -0.06713620  -0.35261164    0.7972728     0.9732278
##                  d
## tau     0.03028121
## alpha  -0.01195278
## a      -3.26006651
## b      38.89424115
## c     111.04029305
## d       0.55414033
##                tau         alpha            a             b            c
## tau    0.025570091 -1.973382e-05 -0.052365829  -0.834029379  -0.10026445
## alpha -0.005634433  4.797222e-04  0.003555771  -0.004613703  -0.02926528
## a     -0.119264181  5.912445e-02  7.539519024 -16.636614000 -45.50200113
## b     -0.512201496 -2.068618e-02 -0.595002439 103.692834678 205.39796269
## c     -0.026633705 -5.675558e-02 -0.703897505   0.856786289 554.24080940
## d     -0.029817572 -5.060586e-02 -0.861469451   0.832870121   0.95576069
##                   d
## tau   -0.0005108497
## alpha -0.0001187546
## a     -0.2534349045
## b      0.9086704009
## c      2.4107553457
## d      0.0114791426
##               tau         alpha            a           b            c
## tau    0.01527304  0.0002214056 -0.100681725 -0.34445406 -0.045997595
## alpha  0.05938036  0.0009102617  0.004027365 -0.00290831 -0.003636241
## a     -0.41726690  0.0683697334  3.811957174 -0.84697948 -1.388952990
## b     -0.80802604 -0.0279456557 -0.125763796 11.89834312  4.219214015
## c     -0.13775367 -0.0446067129 -0.263296020  0.45270893  7.300262789
## d     -0.06993240 -0.0444134044 -0.649613306  0.49882427  0.787787492
##                   d
## tau   -3.602595e-04
## alpha -5.585622e-05
## a     -5.286926e-02
## b      7.172410e-02
## c      8.872635e-02
## d      1.737595e-03
##               tau         alpha             A             k
## tau    0.06503351  0.0003149599   -4.84939308  -0.274028401
## alpha  0.01707841  0.0052297213    0.08019419  -0.008950672
## A     -0.58601184  0.0341736404 1052.99139925 390.856209155
## k     -0.07532640 -0.0086763402    0.84435451 203.497724085
##               tau        alpha             A             k             s
## tau    0.21165272 -0.000426117 -3.925350e+03 -2.081147e+04  4.396630e-03
## alpha -0.01460276  0.004023131  4.118944e+02  2.391752e+03 -7.786722e-04
## A     -0.09642461  0.073388019  7.829919e+09  4.463185e+10 -9.517529e+03
## k     -0.08967919  0.074754103  9.999244e-01  2.544475e+11 -5.438507e+04
## s      0.08647337 -0.111082845 -9.732401e-01 -9.755625e-01  1.221381e-02
##                tau         alpha             a            b             c
## tau    0.214518069 -0.0003550751  -0.538082292  -34.0507812 -1.713471e-01
## alpha -0.011304849  0.0045988268  -0.001952738    0.2165018 -9.010198e-02
## a     -0.108906395 -0.0026993365 113.795938370 -187.2173158 -7.914804e+02
## b     -0.876266309  0.0380521208  -0.209181661 7039.1149112  4.143780e+03
## c     -0.003436565 -0.0123421416  -0.689217871    0.4587936  1.158886e+04
## d      0.004287326 -0.0026532337  -0.865182793    0.4050849  9.433785e-01
##                   d
## tau    3.359598e-04
## alpha -3.044163e-05
## a     -1.561493e+00
## b      5.750080e+00
## c      1.718206e+01
## d      2.862449e-02
##               tau        alpha            A            k
## tau    0.06189590  0.000749934  -19.3766256   0.06735537
## alpha  0.02842076  0.011248975    0.4502756  -0.02288591
## A     -0.79801136  0.043499450 9525.2479320 939.29423390
## k      0.01603255 -0.012778299    0.5699344 285.15256354
##               tau        alpha             a            b            c
## tau    0.12117346 0.0004659518  -2.869971606  -10.5598574   -1.4162456
## alpha  0.01075787 0.0154818231   0.211107563    0.2375863    0.2476308
## a     -0.70648113 0.1453849539 136.190419918  182.2894711   -0.7594473
## b     -0.77293034 0.0486515078   0.397992013 1540.3800963  911.1858983
## c     -0.10776941 0.0527174423  -0.001723793    0.6149697 1425.2090609
## d     -0.09311381 0.0212221632  -0.159757755    0.5087182    0.9108688
##                   d
## tau   -0.0063821151
## alpha  0.0005199331
## a     -0.3670980089
## b      3.9313166965
## c      6.7708302340
## d      0.0387698037
##                tau         alpha           a            b            c
## tau    0.125983768 -0.0003188892 -1.41689490  -5.18807203   0.01574039
## alpha -0.022980088  0.0015284863  0.03441449   0.01682163  -0.04159551
## a     -0.840803518  0.1854064100 22.54092022  49.56743350 -28.24525413
## b     -0.900297860  0.0265017652  0.64305501 263.58759388 168.71913858
## c      0.001599065 -0.0383639752 -0.21451989   0.37472250 769.10244390
## d      0.007372106 -0.0733255715 -0.34398193   0.31617058   0.90706181
##                   d
## tau    0.0003180466
## alpha -0.0003484401
## a     -0.1985013128
## b      0.6239156455
## c      3.0575313187
## d      0.0147735161
##               tau        alpha           a            b            c
## tau    1.12580162  0.001287381 -4.69961198 -18.22958907  -1.51948038
## alpha  0.03114749  0.001517421  0.01319642  -0.02110376  -0.07847249
## a     -0.97272280  0.074398008 20.73404032  74.91340638  -1.13982524
## b     -0.97681561 -0.030801621  0.93537169 309.36181647  84.94681404
## c     -0.06938212 -0.097599543 -0.01212773   0.23398990 426.02319075
## d     -0.04144872 -0.172378031 -0.08748768   0.15390967   0.88230682
##                   d
## tau   -0.0044305334
## alpha -0.0006764705
## a     -0.0401331102
## b      0.2727176141
## c      1.8346371713
## d      0.0101491076
##                 tau        alpha            a            b            c
## tau    4.3654790031  0.001714325 -12.22044683 -59.60602527  0.011697419
## alpha  0.0199343769  0.001694139   0.01017155  -0.01455555 -0.009423365
## a     -0.9889633540  0.041785148  34.97694466 166.48781145 -0.782545650
## b     -0.9962157974 -0.012349045   0.98303894 820.05234162  5.557432082
## c      0.0009932912 -0.040619450  -0.02347584   0.03443149 31.768378767
## d     -0.0141162175 -0.146668035  -0.05483698   0.01995116  0.740111498
##                   d
## tau   -0.0014449615
## alpha -0.0002957549
## a     -0.0158886299
## b      0.0279905154
## c      0.2043697693
## d      0.0024001808
##               tau        alpha            A           k
## tau    0.42581347  0.002555004 -12.70544736   0.9144590
## alpha  0.03997885  0.009591872  -0.09230591  -0.1661125
## A     -0.72331934 -0.035012862 724.60340793 351.9518421
## k      0.06666431 -0.080684364   0.62197351 441.8983042
##               tau       alpha           a            b           c            d
## tau    0.23954039 -0.01240639 -3.06757093 -12.13769640  -0.6793393  0.005296252
## alpha -0.19715142  0.01653151  0.30052853   0.88825621   0.1615168  0.001218204
## a     -0.85319590  0.31818008 53.96509503 146.67611491  -2.6986202 -0.326810904
## b     -0.93435139  0.26028272  0.75225706 704.48752743 124.6222444 -0.100127663
## c     -0.06298735  0.05700561 -0.01667022   0.21306639 485.6103600  3.267978853
## d      0.05462987  0.04783156 -0.22459030  -0.01904445   0.7486627  0.039237213
## png 
##   2
## png 
##   2

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

plot k (stand age at half biomass asymptote)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (productivity trend – in % / year – 2000-2021)

##          region weighted.ge weighted.tau.std_Error 95 % CI, upper
## 1     entire US  0.69247579             0.09453550      0.8777654
## 2       pacific -0.06675040             0.02784261     -0.0121789
## 3          east  0.66813069             0.04057178      0.7476514
## 4 interior west  0.09109551             0.08071977      0.2493063
##   95 % CI, lower
## 1     0.50718621
## 2    -0.12132191
## 3     0.58860999
## 4    -0.06711524

alpha (biomass compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.79932769             1.356089e-07     0.79932796
## 2       pacific     0.08789315             5.175654e-03     0.09803743
## 3          east     0.62778715             5.008890e-03     0.63760458
## 4 interior west     0.08364739             2.998747e-03     0.08952494
##   95 % CI, lower
## 1     0.79932743
## 2     0.07774887
## 3     0.61796973
## 4     0.07776985

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   459.2681
## 2       pacific  1418.2708
## 3          east   377.0926
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   360.2866
## 2       pacific   314.7279
## 3          east   395.6918
## 4 interior west   188.0424

Model Bookeeping

1. Empirical Delta-B total

2. Delta-B due to Delta-STDAGE

3. Delta-B due to Delta-Year (ge)

Delta B constants

FUNCTION: simulate f(age) – accounting for uncertainty in the age function – rmvnorm

solve for f(age)

5. Delta B due to B_l

BK_df

Delta B

## Warning: Removed 12044 rows containing missing values (`geom_point()`).

## Warning: Removed 12044 rows containing missing values (`geom_point()`).

## Warning: Removed 6022 rows containing missing values (`geom_point()`).

## Warning: Removed 12044 rows containing missing values (`geom_point()`).

## Warning: Removed 32294 rows containing missing values (`geom_point()`).

Stand age densities

## Warning: package 'ggridges' was built under R version 4.2.2
## Picking joint bandwidth of 4.71
## Picking joint bandwidth of 9.91
## Picking joint bandwidth of 11.6
## Warning: Removed 90 rows containing non-finite values (`stat_density_ridges()`).
## Warning: Using the `size` aesthietic with geom_segment was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.

Delta B age vs. Delta Stand age

## `geom_smooth()` using formula = 'y ~ x'

## Warning: Removed 32294 rows containing missing values (`geom_point()`).
## Picking joint bandwidth of 4.71
## Picking joint bandwidth of 9.91
## Picking joint bandwidth of 11.6
## Warning: Removed 90 rows containing non-finite values (`stat_density_ridges()`).

## Warning: Removed 12044 rows containing missing values (`geom_point()`).
## Picking joint bandwidth of 4.71
## Picking joint bandwidth of 9.91
## Picking joint bandwidth of 11.6
## Warning: Removed 90 rows containing non-finite values (`stat_density_ridges()`).
## png 
##   2

```